Modern interconnected systems and networks are growing more pervasive and complex by the day. While this is rendering data more abundant, its structure is more intricate than the one exhibited by classical datasets. Relying on graphs to model irregular information domains has emerged as a successful and tractable approach to deal with some of the challenges present in contemporary datasets. This approach, which has a long history in statistics [1]}, has been recently gaining traction in the machine learning [2]}, [3]} and signal processing communities [4]}. In the latter case, graph signal processing (GSP) puts forth a systematic approach where variables are modeled as nodes, the information domain is modeled as a graph (so that the focus is on sparse heterogeneous relations among pairs of variables), and the data itself is modeled as graph signals. Graph signals are abundant in nature, including the congestion levels in a telecommunication network, the electrical neurological activity in a brain network, and the information being diffused across the agents of a social network, to name some diverse examples. The key in GSP is to postulate meaningful and tractable: i) models relating the properties of the data with the properties of the graph and ii) graph-signal operators that depend on the topology of the graph [5]}, [6]}, [7]}. With these two ingredients, a number of GSP-related problems have been investigated, ranging from basic sampling and reconstruction schemes [8]}, [9]}, [10]} to advanced deep graph neural network architectures [11]}, [12]}, [13]}. An area of particular interest is that of linear graph filters and their application to model linear network dynamics and solve inverse GSP-related problems. Mathematically, graph filters are graph-signal operators that can be represented by a matrix that is a polynomial of either the adjacency or Laplacian matrix of the graph [4]}, [5]}, [16]}. Practically, they can be implemented distributedly, account for a multi-resolution (multi-hop) description of the graph, and can capture spatio-temporal dynamics taking place across the nodes (agents) of a network [17]}, [18]}, [19]}. As a result, there has been a growing interest in using graph filters to postulate generative models of graph signals [4]}, [21]}, [22]}. The most widely-used approach is to model the signal at hand as the output of a graph filter excited with a parsimonious (e.g., sparse, white, or bandlimited) input graph signal. One can then formulate a number of inverse problems where (an imperfect version of) the output graph signal is given and, depending on the particular setup and the variables that are known, the goal is to recover the filter, the input, the parts of the output that are unknown or any combination thereof [22]}. When the input graph signal is sparse (i.e., there are only a few nodes -sources- with a non-zero value), the associated output is referred to as a diffused graph signal, with sampling, reconstruction, blind deconvolution and filter identification of diffused graph signals having been investigated in detail [24]}, [25]}, [26]}, [27]}.
